The inventory of homes for sale continued to shrink, down to a 4.4 month supply in December based on the month's sales pace. That's down from 4.8 months in November and is the lowest level since May 2005. Realtors consider a 6-month supply to be a balanced market between buyers and sellers.

Homes are selling faster than a year ago. The median time on the market for all homes was 73 days last month compared with 99 days in December 2011. According to NAR, 31% of all homes sold in December were on the market less than a month.

Single-family home sales slipped 1.4% to a seasonally adjusted annual rate of 4.35 million in December from 4.41 million in November, but are 11.5% above the December 2011 pace, NAR says.

The median existing single-family home price was $180,300 in December, up 11.5% from a year ago. Median prices are affected by the mix of homes sold and can go up or down depending on whether higher-priced homes make up more of the market.

Distressed homes - foreclosures and short sales - accounted for 24% of December's sales, down from 32% in December 2011. Foreclosures sold for an average discount of 17% below market value while short sales went for 16% under market value. Short sales are homes that are sold for less than their unpaid mortgage amount.

Market researcher CoreLogic, whose data includes repeat sales of like homes, says home prices in November were up 7.4% year over year.

The housing market has become a bright spot in the U.S. economy after a six year down draft that reduced national home prices more than 30%.

Tightened inventories of homes for sale - and fewer distressed properties on the market - have helped lift prices.

Improving job growth, low interest rates and rising prices are convincing more people that the market has bottomed and that it's time to buy.

Other recent reports also show strengthening in the housing market.

While new home construction is still far from healthy levels, builders started work on homes in December at the fastest pace since the summer of 2008, the Commerce Department said last week.

Home builder sentiment in January remained at a six-year high but didn't move higher as it had in previous months, the NAHB/Wells Fargo Housing Market Index also showed last week.

CoreLogic expects national home prices to rise 6% this year, on top of a 7.5% increase last year.

Yet the tight supply of homes for sale is a big concern in many markets where rapidly shrinking inventories are leading to multiple offers and higher prices.

In California, one state where foreclosures progress faster because they don't go through the courts, the supply of homes for sale in December fell to 2.6 months, down from 4.3 months a year earlier, the California Association of Realtors reported.

Rising home prices should eventually encourage more owners to list their homes for sale, CoreLogic says.